I just found the Laurent series for $z^{2}e^{1/z}$ for $z = 0$, and now I need to find it at $z = \infty$. (for $z=0$, it was $\displaystyle \sum_{n=0}^{\infty}\frac{z^{2-n}}{n!}$, by the way).
I'm not sure how to approach this problem for $z = \infty$, however...
I came across one method involving finding the series for $\zeta^{-2}(f(\zeta^{-1}))$. Apparently, this gives the series at $\infty$, but I don't really understand how.
Please help - full, detailed solution preferred. I am extremely confused and am trying to teach myself this stuff; it helps me to see fully worked out examples. Thank you.